This collection of high-quality articles in the field of combinatorics, geometry, algebraic topology and theoretical computer science is a tribute to Jiří Matoušek, who passed away prematurely in March 2015. It is a collaborative effort by his colleagues and friends, who have paid particular attention to clarity of exposition – something Jirka would have approved of.

The original research articles, surveys and expository articles, written by leading experts in their respective fields, map Jiří Matoušek’s numerous areas of mathematical interest.

Jiří Matoušek studied at Charles University in Prague, where he also took his doctorate and worked since 1986 till his early decease. He was a full professor at Charles University since 2000. Since 2012 he was also a full professor at ETH Zurich.

He was internationally very active, visited many institutions and delivered distinguished lectures, for example, at the European Congress of Mathematicians in 1996 and at the International Congress of Mathematicians in 1998. He was awarded the Prize of EMS for young researchers in 1996 and the Prize of the Czech Learned Society in 2000.

Jiří Matoušek was a brilliant and outstanding mathematician and computer scientist. Although his research focused on combinatorics, discrete geometry and algorithmics, his interests ranged well beyond these areas. He was a recognised expert in fields including algorithmic geometry, topological methods, discrepancy theory and linear programming.